Semiconductor amplifying elements, such as bipolar and field effect transistors, adapted for microwave frequencies, in the range of 200 megahertz to 2 gigahertz, are inherently unstable over at least a portion of the normal useful frequency band thereof because they have high gain and parasitic feedback impedances. Typically, such microwave amplifying elements are connected to a microwave source by a first tuned impedance, and to a microwave load through a second tuned impedance. For efficiency purposes, it is desirable for the first tuned circuit to provide matching between the microwave source and input and common terminals of the amplifier, and for the second tuned circuit to provide matching between the load and output and common terminals of the transistor amplifying element. In the past, however, providing such matching networks has been done at the sacrifice of stability to the amplifier over at least a portion of its desired operating range. Hence, to provide stability, it has frequently been the practice to selectively mismatch the source and/or load to the input, output and common electrodes of the amplifying element. It has been found that such selective mismatching, in addition to decreasing the amplifier efficiency, has the further disadvantage of providing voltage standing-wave ratio changes to the input and output electrodes of the amplifier sufficient to cause oscillations and, therefore, instability over at least a portion of the amplifier frequency range.
The mismatch concept is basically discussed in:
BSTJ, Volume 35, pages 813-40, July 1956, J. G. Linvill et al, article entitled "The Design Of Tetrode Transistor Amplifiers;" PA1 the book Transistors And Active Circuits, published by McGraw-Hill, 1960, written by J. G. Linvill et al; and PA1 Motorola Application Note Number 166, 1967, entitled "Using Linvill Techniques For RF Amplifiers," written by P. M. Norris. PA1 Proceedings Of The Institute of Radio Engineers, Volume 45, pages 335-343, March 1957, in an article entitled "Stability And Power Gain Of Tuned Transistor Amplifiers," written by A. P. Stern; PA1 the book Principles And Design Of Linear Active Circuits, published by McGraw-Hill, 1965, written by M. S. Ghausi; and PA1 Motorola Technical Application Note 215, 1967, entitled "RF Small Signal Design Using Admittance Parameters" written by R. Hejhill. PA1 g.sub.22 =the conductance between the output and common electrodes of the device, PA1 Re=real component, PA1 y.sub.21 =forward transfer admittance of the device from the input to the output electrodes thereof, and PA1 y.sub.12 =reverse transfer admittance of the device from the output to the input electrodes thereof. PA1 G.sub.22 =the shunt conductance between the transistor output and common electrodes. PA1 C.sub.1 * and C.sub.2 * are respectively complex conjugates of C.sub.1 and C.sub.2 PA1 S.sub.11 * and S.sub.22 * are respectively complex conjugates of S.sub.11 and S.sub.22 PA1 S.sub.11 and S.sub.22 are respectively reflection coefficients of the element and resistor means between the input and common electrodes and between the output and common electrodes PA1 S.sub.12 and S.sub.21 are respectively the reverse and forward transmission coefficients of the element and resistor means, whereby .vertline.S.sub.12 .vertline..sup.2 and .vertline.S.sub.21 .vertline..sup.2 are respectively reverse and forward insertion power gains of the element and resistor means, and PA1 .angle.S.sub.12 and .angle.S.sub.21 are respectively reverse and forward insertion phase shifts of the element and resistor means
In accordance with another technique, attempts to stabilize microwave, semiconductor amplifiers are made by mismatching source and load impedances by conductive loading. This technique, known as Stern's stability method, is reported in:
The Stern's stabilization method achieves network stabilization by mismatching the source and load impedances at the expense of amplifier gain. If a semiconductor, microwave amplifier element is potentially unstable, source and load admittances can be selected to insure unconditional stability of the amplifier device. An amplifier element is defined as being unconditionally stable if no combination of passive source or load impedances can be found which causes the device to oscillate. Stated differently, an unconditionally stable transistor network cannot be made to oscillate with any combination of load and source impedances without the application of external feedback. A linear two-port device, such as a microwave transistor amplifier element, is unconditionally stable if the real part of the impedance or admittance looking into either the input or output port of the device is positive for any passive termination of the other port. A linear two-port device is conditionally stable, i.e., potentially unstable, if the real part of the impedance or admittance looking into either the input or output port of the device is positive for some, but not all, passive terminations of the other port. If the real part of the impedance looking into a port is positive, the magnitude of the reflection coefficient looking into that port must be less than 1, i.e., the reflection coefficient must remain on a Smith chart. A linear two-port device, such as a class A linear microwave transistor amplifier, is therefore unconditionally stable if the reflection coefficients for the input and output terminals of the device, as mapped on a Smith chart, lie on the Smith chart for any value of passive load or source impedance. A linear two-port device is conditionally stable if the reflection coefficients looking into input and output terminals of the device lie on the Smith chart for only some values of load or source impedance, and lie off of the Smith chart for other values of load or source impedance.
Amplifiers designed in accordance with Stern's Stabilization Method, in addition to having relatively poor gain properties, are not always stable. In particular, in one device that was theoretically calculated utilizing a Hewlett Packard HXTR-6101 common emitter microwave transistor operating at one gigahertz it was found that there was conditional stability for source and load impedances of 50 ohms each, shunt input and output reactances of 4.127 and 4.37 millimhos, respectively, and perfect matching transformers having turns ratios of 3.96:1 and 7.34:1 between the source and input and between the load and output of the amplifying device, respectively.
In addition to the aforementioned disadvantages, Stern's stabilization method requires the use of one or more padding resistors external to a package in which the active semiconductor amplifying element is located. External resistors to the semiconductor amplifying element package increase the values of parasitic reactive components, particularly inductance, due to lead lengths. Of course, changing the parasitic reactance associated with the amplifying element has a change and substantial effect on the characteristics of a microwave device, so that the microwave semiconductor amplifier is not likely to operate in accordance with its theoretical, calculated performance. In addition, in the Stern's stabilization method, the value of a padding resistor or resistors is selected somewhat arbitrarily and then verified either empirically or iteratively with the use of a computer analysis. Such procedures increase the design time and prevent optimum stability and gain performance.
Rollett has reported a precise, mathematical stability factor related to the admittance parameters of a two-port device, such as a linear transistor microwave amplifier. Rollett's stability factor is reported in The Institute Of Radio Engineers' Transactions On Circuit Theory, CT-9, pages 24-32, March 1962, in an article entitled "Stability And Power Gain In Variance Of Linear Two-Ports." Rollett's stability factor, K, can be expressed as: ##EQU1## where g.sub.11 =the conductance between input and common terminals of the device,
If the value of K is greater than 1, the device is unconditionally stable. If the value of K is less than 1, the device is conditionally stable, and therefore subject to oscillation under certain load conditions. Of course, load conditions can vary in a real device; for instance, if the load is an antenna, weather and/or proximity of the antenna to other structures change the load impedance.
Rollett's stability factor can be rewritten in terms of s-parameters, which are reflection and transmission coefficients directly related to voltage standing-wave ratios and impedances, particularly of microwave semiconductor amplifying devices operating under linear conditions. As described in Hewlett Packard Application Note 95 entitled "S-Parameters . . . Circuit Analysis and Design," published September 1968, s-parameters are vector quantities providing magnitude and phase information. Two-port s-parameters are easy to measure at high frequencies because a device under test is terminated in the characteristic impedance of a measuring system for the device. A two-port device can be defined by four s-parameters, s.sub.11, s.sub.22, s.sub.12, s.sub.21 ; s.sub.11 and s.sub.22 are input and output reflection coefficients of the two-port device; s.sub.12 and s.sub.21 are respectively the reverse and forward transmission coefficients of the device whereby .vertline.s.sub.12 .vertline..sup.2 and .vertline.s.sub.21 .vertline..sup.2 are respectively reverse and forward power gains of the device and .angle.s.sub.12 and .angle.s.sub.21 are respectively reverse and forward insertion phase shifts of the device. Because admittance (y, g and b) parameters can be transformed into scattering (s) parameters, Rollett' s stability factor can be rewritten as: ##EQU2## where D=s.sub.11 s.sub.22 -s.sub.12 s.sub.21.
Rollett extended the stability factor relationship as a function of admittance to include passive terminations connected in shunt with input and output ports of a transistor, i.e., to resistors in shunt between input and common electrodes of the transistor and between output and common electrodes of the transistor. In such a case Equation (1) can be rewritten as: ##EQU3## where G.sub.11 =the shunt conductance between the transistor input and common electrodes; and